Lambert-Beer's Law PDF | Chemistry

UCB009-CHEMISTRY Lambert Beer’s Law / Beer’s Law UCB009_2425EVESEM A brief outline: Introduction to absorption of light Definition and derivation of Lambert-Beer’s Law / Beer’s Law Relationship between absorbance and transmittance A plot of transmittance and abso...

UCB009-CHEMISTRY Lambert Beer’s Law / Beer’s Law UCB009_2425EVESEM A brief outline: Introduction to absorption of light Definition and derivation of Lambert-Beer’s Law / Beer’s Law Relationship between absorbance and transmittance A plot of transmittance and absorbance vs sample concentration Properties and units of molar absorption coefficient Application of Beer’s Law Limitations of Beer’s Law UCB009_2425EVESEM  Absorption of Light If the sample does not Incident light intensity at Transmitted light intensity absorb the incident light a particular wavelength at the same wavelength I = I0 If the sample absorbs the incident light I ≠ I0; I < I0 Recall: Intensity = |Amplitude|2  Absorption  Intensity Note: Transmitted intensity decreases with respect to the Incident intensity Wavelength remains constant or unchanged upon absorption Lambert-Beer’s Law / Beer’s Law A=εcl A= absorbance ε = molar absorption coefficient c = concentration l = path length Definition of Lambert-Beer’s Law / Beer’s Law When a beam of monochromatic radiation passes through a dilute solution of an absorbing substance, then the rate of decrease of intensity of radiation with the thickness of the absorbing medium is directly proportional to the intensity of incident radiations and concentration of the solution. (OR) The intensity of a beam of monochromatic radiations decreases exponentially with an increase in the thickness and the concentration of the dilute absorbing solution UCB009_2425EVESEM Derivation of Lambert-Beer’s / Beer’s Law Factors Affecting the Transmitted Light Intensity ❖ Thickness of sample/Path length ❖ Concentration of Sample/Analyte Let I0 and I be the intensity of incident and transmitted radiation, respectively, x be the thickness, and c be the concentration of the solution (-)dI = = + + Hypothetical dx slicing where (-)dI is the change in intensity upon absorption of incident radiation on passing through a thickness dx of the solution Derivation of Lambert-Beer’s / Beer’s Law 𝑑𝐼 𝑑𝐼 𝑑𝐼 ‘K’: proportionality − ∝ 𝑐𝐼  − = 𝐾𝑐𝐼  − = 𝐾𝑐𝑑𝑥 𝑑𝑥 constant. 𝑑𝑥 𝐼 Note: The minus sign is introduced because there is a reduction in the intensity upon absorption Integrating the equation between limit I = I0 at x = 0 and I = I at x = 𝑙 we get, 𝐼 𝑑𝐼 𝑥=𝑙 න− = 𝐾𝑐 න 𝑑𝑥 𝐼0 𝐼0 𝐼 Absorbance (A) = log10 where, log10 = 𝜀𝑐𝑙 𝐼0 𝑥=0 𝐼 𝐼 𝐼  ln = −𝐾𝑐𝑙 𝐼0  𝐀 = 𝜺𝒄𝒍 Lambert Beer ’s Law eqn. 𝐼  ln 0 = 𝐾𝑐𝑙 𝐼 where, A = Absorbance 𝐼0  = Molar absorption coefficient  2.303 log10 = 𝐾𝑐𝑙 c = Concentration of the sample/analyte 𝐼 l = Path-length of the solution 𝐼0 𝐾  log10 = 𝑐𝑙 Based on these equations, we can also write 𝐼 2.303 𝐼0 𝐾 𝐼 𝐼  log10 = 𝜀𝑐𝑙 𝑎𝑠 =𝜀 Transmittance (T) = where, = 𝑒 −𝐾𝑐𝑙 𝐼 2.303 𝐼0 𝐼0 UCB009_2425EVESEM Relationship between Absorbance and Transmittance 𝐼 𝐼0 As we already know; T= and A = log10 𝐼0 𝐼 1 1 Hence, we may write: A = log10 𝐼 = − log10𝑇  T = 10-A = 10-cl = log10 𝐼0 𝑇 %𝑇 If Transmittance is expressed in percentage as %T = T x 100  T = 100 1 1 Hence, we may rewrite the eqn. 𝐴 = log10 as: A = log10 %𝑇 = log10100 − log10%T 𝑇 100 or, A = 2 − log10%T Relationship between Absorbance and Transmittance vs concentration 𝐼 𝐼0 Recall T = = 𝑒 −𝐾𝑐𝑙 Recall log10 = 𝐴 = 𝜀𝑐𝑙 𝐼 𝐼 0 𝐼  = 𝑇 ∝ 𝑒 −𝑐𝑙 𝐼0 (since ‘K’ is a constant) Concentration Concentration  Key-points for Solving Beer’s Law Numericals 𝐼 𝐼0 As we already know; T = and A = log10 𝐼0 𝐼 Conversion (Numericals) Represents double-headed arrow (e.g. Two-way traffic) (Transmittance) T ✓ (Percent Transmittance) %T (%T = 100 x T) ✓ (A = -log10T) ✓ (Applicable) or, (%A = 100 - %T) (T = 10-A) (Applicable) (Applicable) A % A’ (Percent Absorption)  (Absorbance) To calculate %A’ from A (Not Applicable) Take a detour via A → T → %T → %A’ UCB009_2425EVESEM Properties and Units of Molar Absorption Coefficient 1. Units of Molar absorption coefficient A =  cl   = A cl According to convention; the unit of c is Molar (M) = mol/L = mol/dm3 the unit of l is a centimeter (cm) and Absorbance is a dimensionless quantity The units of  is = M-1cm-1 = Lmol-1cm-1 = dm3mol-lcm-l = cm2mol-l 2. Properties of Molar absorption coefficient ❖ Constant Absorbance Slope = l ❖ Molecule-specific ❖ Wavelength-dependent Concentration (M) How do we use Beer-Lambert Law ? 1. Numerical A monochromatic radiation is incident on a solution of 0.05 molar concentration of an absorbing substance. The intensity of the radiation is reduced to one fourth of the initial value after passing through 10 cm length of the solution. Calculate the molar extinction coefficient of the substance……….. 2. Finding the unknown A = εcl ---➔ Lambert-Beer Law: Proof-of-concept experiment in Chemistry Lab Ferroin (Redox indicator) UCB009_2425EVESEM Augustina et al. ChemistryOpen 2015; DOI: 10.1002/open.201500096 Limitations of Lambert-Beer Law Beer’s law is applicable to dilute solutions only The radiation should be monochromatic Solute must not undergo association, dissociation, polymerization, or hydrolysis in the solvent 1. State Lambert-Beer’s law. What do you mean by absorbance and transmittance? 2. What are the units used for the Molar Extinction Coefficient? 3. The molar extinction coefficient of Coen2Br2+ is 40 M-1 cm-1 at 650 mμ (milli micron). Calculate the percent transmission for a 5 cm cell filled with 0.01 M solution. What will be the corresponding absorbance? 4. A 0.003 M solution of [Co (NH3)6]3+ transmits 75% of incident light of 500 mμ if the path length is 1 cm. Calculate the molar extinction coefficient and the percent absorption for a 0.01 M solution. 5. A substance in an aqueous solution at a concentration of 10-3 M absorbs 10% of incident light in a path length of 1 cm. What concentration will be required to absorb 90% of the light? 6. At 460 nm, a blue filter transmits 72.7% of the light, and a yellow filter transmits 40.7% of the light. What is the transmittance at the same wavelength of two filters in combination? UCB009_2425EVESEM